complex number

[nidhi]

the complex number z=a+ib satisfy arg(z square minus 4)=5 pie/6 and arg(z square plus 4)= pie/3 then the value of a square plus b square is

[factor-fiction]

This is the third one I've seen nidhi.
I have given big hints with one.
Try squaring both sides of the initial equation andthen compare coefficients to see what this tells you about and b

[factor-fiction]

A big hint for you:
(a+bi)(a-bi) = a² + abi - abi - b²i² = a² + b²